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Origami and Kirigami, the famous Japanese art forms of paper folding and cutting, have inspired the design of novel materials & structures utilizing their geometry. In this article, we explore the geometry of the lesser known popup art,…
Origami and kirigami have emerged as potential tools for the design of mechanical metamaterials whose properties such as curvature, Poisson ratio, and existence of metastable states can be tuned using purely geometric criteria. A major…
Current architectured cellular cushion materials rely mainly on damage and/or unpredictable collapse of their unit cells to absorb and dissipate energy under impact. This prevents shape recovery and produces undesirable force fluctuations…
Colloidal self-assembly allows rational design of structures on the micrometer and submicrometer scale. One architecture that can generate complete 3D photonic band gaps is the diamond cubic lattice, which has remained difficult to realize…
We present a general and modular algorithmic framework for path planning of robots. Our framework combines geometric methods for exact and complete analysis of low-dimensional configuration spaces, together with practical, considerably…
We systematically investigate the electronic structure, magnetism and high-temperature superconductivity (SC) in the multi-layer octagraphene and octagraphite (bulk octagraphene). A tight binding model is used to fit the electronic…
It is well-known that the Kresling pattern of congruent triangles can be arranged either circularly on a cylinder of revolution or in a helical way. In both cases the resulting cylindrical structures are multi-stable. We generalize these…
Extreme deformation can drastically morph a structure from one structural form into another. Programming such deformation properties into the structure is often challenging and in many cases an impossible task. The morphed forms do not hold…
This study explores the use of origami composite structures as active aerodynamic control surfaces. Towards this goal, two origami concepts were designed leveraging a combination of analytical and finite element modeling, and computational…
The functionality of catalysts, enzymes, and supramolecular assemblies emerges not from individual molecules alone, but from the subtle interplay between multiple components arranged in complex systems. Designing such systems is a grand…
Rigid origami has shown potential in large diversity of practical applications. However, current rigid origami crease pattern design mostly relies on known tessellations. This strongly limits the diversity and novelty of patterns that can…
Cells and microorganisms employ dynamic shape changes to enable steering and avoidance for efficient spatial exploration and collective organization. In contrast, active colloids, their synthetic counterparts, currently lack similar…
We have developed a software MagGene to predict magnetic structures by using genetic algorithm. Starting from an atom structure, MagGene repeatedly generates new magnetic structures and calls first-principles calculation engine to get the…
Advances in 3D printing technology now enable the precise positioning of microscopic material voxels to form complex structures. Combined with emerging multi-material capabilities and printable responsive materials, this opens new…
DNA self-assembly is an important tool that has a wide range of applications such as building nanostructures, the transport of target virotherapies, and nano-circuitry. Tools from graph theory can be used to encode the biological process of…
Legged robot locomotion requires the planning of stable reference trajectories, especially while traversing uneven terrain. The proposed trajectory optimization framework is capable of generating dynamically stable base and footstep…
Transforming planar mesoscale devices into precise 3-D architectures is vital for next-generation flexible electronics, implants, and adaptive optics, yet wafer-based manufacturing to free-standing 3-D structures remain elusive. We…
A stacking operation adds a $d$-simplex on top of a facet of a simplicial $d$-polytope while maintaining the convexity of the polytope. A stacked $d$-polytope is a polytope that is obtained from a $d$-simplex and a series of stacking…
Like the letters in the alphabet forming words, reusing components of a heterogeneous mixture is an efficient strategy for assembling a large number of target structures. Examples range from synthetic DNA origami to proteins self-assembling…
This paper presents a novel decoder-based approach for generating manufacturable 3D structures optimized for additive manufacturing. We introduce a deep learning framework that decodes latent representations into geometrically valid,…